Evaluate the indefinite integral.

Question

mony01 · Answer

$$\int\limits (x ^{2}+1)(x ^{3}+3x)^{4}dx$$

anonymous · Answer

Substitute $u=x^3+3x$ and differentiate this with respect to $x$, try to use this substitution to solve your problem.

mony01 · Answer

ok is du=3x^2 + 3dx and dx=1/3x^2 +1/3

anonymous · Answer

$$\large \frac{du}{dx}=3x^2+3 = 3(x^2+1) \implies \frac{1}{3}\frac{du}{dx}=\underbrace{x^2+1}_! $$

anonymous · Answer

you see how to use this for your integral? $$ \large\int\limits \underbrace{(x ^{2}+1)}_!(x ^{3}+3x)^{4}dx $$

mony01 · Answer

yeah i see

mony01 · Answer

so how would the integral look like, would it look like$$\frac{ 1 }{ 3}\int\limits (u)^{4}du$$

anonymous · Answer

exactly

anonymous · Answer

which is very easy to integrate, just remember the basic rule of thumb "Every substitution requires a back substitution". So evaluate the above integral and then back substitute your $u$